Which equation is true?

By solving equations, we know that the number of apples and mangoes purchased is 8 and 2, respectively.

In a mathematical equation, the equals sign is used to express that two expressions are equal.

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.

For instance, the expressions 3x + 5 and 14 make up the equation 3x + 5 = 14, with the word "equal" separating them.

So, we know that:

Apple and mango are worth $13.50.

Each mango costs $0.75, but each apple costs $1.50.

Let the number of apples be x and the number of mangoes be y, so that:

1.50x + 0.75y = 13.50

Fewer apples than mangoes by six That is to say,

x = y + 6

x - y = 6

The two resulting equations are:

1.50x + 0.75y = 13.50

x - y = 6

The simultaneous equation's solution provides

x = 8

y = 2

Therefore, by solving equations, we know that the number of apples and mangoes purchased is 8 and 2, respectively.

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The percentage of the blue blanket will be 25%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that a bin at a department store contains blue and red blankets. The ratio of blue blankets to red blankets is 4 to 1.

The percentage of the blue blanket will be calculated as,

Percentage = 1 / 4

Percentage = 0.25

Percentage = 0.25 x 100 = 25%

Therefore, the percentage of the blue blanket will be 25%.

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Answer:

g = 48

Step-by-step explanation:

60/3 = g-8/2

20 = g-8/2

40 = g-8

g = 48

Answer:

g = 28

Step-by-step explanation:

60 ÷ 3 = g - 8 , that is

20 = g - 8 ( add 8 to both sides )

28 = g

The equation is 26 = 13.5 + 2.5 m, and the value of m is 5, so option C is correct.

Equations are statements in mathematics containing the equals (=) sign flanked on either side by two algebraic expressions. The relationship between the expressions printed on the left and right sides is shown to be equal in this way.

Given:

Twenty-six equals the sum of [tex]13.5[/tex] And the quotient of a number and [tex]2.5.[/tex]

Write the equation in mathematical form,

26 = 13.5 + quotient × 2.5

Assume the quotient is m then,

26 = 13.5 + 2.5 m,

Solve the equation to get the value of m,

26 - 13.5 = 2.5 m,

m = 5

Therefore, the equation is 26 = 13.5 + 2.5 m, and the value of m is 5.

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Answer:

Step-by-step explanation:

a.) The population is years measured after 2000 so 2000 is 0. Any number to the 0 power is 1 so the population is 23.1 (million).

28.3 = [tex]23.1e^{0.0152t}[/tex]

1.22510823 ≈ [tex]e^{0.0152t}[/tex]

ln 1.22510823 ≈ 0.0152t

t≈13.4 million

Answer:

D

Step-by-step explanation:

if u calculate 20×0.4 it will give you 8

the 0 before 8 is insignificant

Answer:

B. 0.2

Step-by-step explanation:

(?) x 0.4 = .08

Reverse math

.08 divided by 0.4

The original price would typically be less expensive than the current price, though it is possible for the two to be equal in specific circumstances. The original price of the pants is $ 19

A store has 20% off sale on pants. With this discount, the price of one pair of pants before tax is $15.20.

n  is the total price, 0.2n is the discount:  n - 0.2n

n - 0.2n = 15.20

Step 2:  Combine like terms

n - 0.2n = 15.20

0.8n = 15.20

Step 3:  Divide both sides by 0.8

0.8n / 0.8 = 15.20 / 0.8

n = 19

$19 is the original price

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If the rectangle JKLM is similar to rectangle WXYZ , then the scale factor is 1.5  .

In the question ,

two rectangle figures are given ,

the rectangles JKLM and WXYZ are similar ,

So , to find the scale we consider the ratio of the sides of the rectangle .

the ratio of the sides is ⇒ ZW/JM = WX/JK

Substituting the values of ZW = 13.5 , JM = 9 , WX = 18 and JK = 12 ,

we get ,

13.5/9 = 18/12

⇒ 1.5 = 1.5

So , the rectangles are similar and the scale factor is = 1.5 .

Therefore , the scale factor is 1.5 .

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The arcs with the same radius from each endpoint, C. make the intersection of the arcs equidistant from the endpoints

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. Another line segment is split into two equal portions by a perpendicular bisector, which intersects it at a 90-degree angle.

The arcs with the same radius from each endpoint make the intersection of the arcs equidistant from the endpoints and we obtain a line segment that is perpendicular to the line segment from we take the measurement of arcs.

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Danielle didn't change the length of triangle then he draw that infinite triangles with given measure.

What is right triangle?

A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles. it.

Given:

Danielle wants to construct different triangles with angle measures of

90°, 45°, and 45°. She was only able to draw the triangle shown at the right.

She did not consider that the triangle could be enlarged or reduced, while keeping the same angle measures, to make a different triangle.

Hence, Danielle didn't change the length of triangle then he draw that infinite triangles with given measure.

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Correct this group constitutes a sample of all students in the class.

What are some instances of intuitive reasoning?

As an illustration, when we enter a coffee shop, we immediately recognize a cup as one that we have seen many times before.

                           We also immediately recognize that it will probably be hot and spill quickly over an uneven surface.

What is the intuitional method?

Intuition is the earliest means of knowing. When we use our intuition, we are putting our trust in our feelings, emotions, and/or instincts to lead the way.

                          When using intuition, one believes what seems true rather than looking at the facts or using reason.

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The required will the act be paid for their performance is $540,000.

In mathematics, a percentage is a number or ratio that can be communicated as a negligible portion of 100. In the event that we need to compute percent of a number, partition the number by the entire and duplicate by 100. Consequently, the rate implies, a section for every hundred

The total amount that should be paid is the sum of the single appearance fee, the 20% of ticket sales and the 10% of concession receipts.

We have,

single appearance = $250,000

sales =$1,250,000

concession receipts = $400,000

Total amount = single appearance + (10% of sales) + (10% ofconcession receipts)

Then,

Total amount = $250,000 + (20% x 1,250,000) + (10% x $400,000) = $540,000

Thus, required total amount is  $540,000.

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The equation written in slope-intercept form withn a slope of -5 and a y-intercept of 5 is y = -5x + 5

intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.

equation of straight line in slope intercept form is given as

y = mx + c

where m = slope and c = y-intercept

from the question, it means m = -5 and c = 5

substituting we have,

y = -5x + 5

In conclusion, the equation in slope-intercept form is y = -5x + 5

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The annual cost is $275,000.

What is annual cost ?

Annual Costs refers to the sum of 1) Authorized Services for each Fiscal Year. 2) Administrative Costs; 3) any sums required to make up for actual or anticipated Special Tax Delinquencies for the current or preceding Fiscal Year.

The charge per square foot is $5.

The total square feet leased

=275ft x 200ft

=55,000 square ft.

The total cost of the annual rent is

=55,000 x $5

=$275,000

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Answer:

43.2ft

Step-by-step explanation:

1in=10.8

4in=4*10.8

Width=4*10.8

Width=43.2

The value of x for the given expression is,  x = 4 / (3√2 - √3).

What is solving an equation?

A General Rule for Equation Solving:

Simplify each side of the equation by removing parentheses and combining like terms.

To separate the variable term on one side of the equation, use addition or subtraction.

To find the variable, use division or multiplication.

Given;

√3x + 2 = 3√2x - 2

⇒

3√2x - √3x = 2 + 2

(3√2 - √3)x = 4

Divide both sides by 3√2 - √3

⇒  x = 4 / (3√2 - √3)

Hence, the value of x for the given expression is,  x = 4 / (3√2 - √3).

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Angle ACD is congruent to angle ADC by transitive equality if angles 1 and 2 are both ACD because angle ACB is congruent to angle ADE in the step above. Therefore, angle 1 equals angle 2, as you can see.

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

Here,

Given that segments AB and AE are congruent, the triangle ABE is required to be isosceles by definition.

As a result, angle ABC must be similar to angle AED, again in accordance with the definition of an isosceles triangle.

Consequently, triangle ABC must be congruent to triangle AED by SAS as you have been informed that segments BC and DE are congruent. Right now, it's unclear to you whether angle 1 is ACB or ACD.

Assuming it is ACB, CPCT shows that ACB is congruent to ADE. Angle 1 equals angle 2, so there you have it. Since angle ACB is supplementary to angle ACD and angle ADE is supplementary to angle ADC.

Since angle ACB is congruent to angle ADE from the step above, angle ACD is congruent to angle ADC by transitive equality if angle 1 and angle 2 are both ACD. Angle 1 equals angle 2, so there you have it.

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She can spend a maximum of $2763.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.

The credit card works as there can be a negative balance in the card. For example if Sally has a shortage of money and she is in need of some, she can take money from her credit card and then repay it later.

Sally already has $763 in her possession in this situation, and her credit card can only have a $2000 balance.

So Sally can spend $763 which she already has in her hand and then spend a maximum of $2000 using her credit card.

Given,

credit card limit = 2000

current balance = 763

2000+763=2763

So She can spend a maximum of $2763.

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The inequality that represents Charlotte having money left over after buying the ticket. is

8m + 20 < 68

Inequality is a means of representing the relationship existing between the left hand side and right hand side of equations, using other terms aside exactly using only "equal to"

Having left over means that the the cost of the ticket should be less than the amount Charlotte has

Therefore, 8m + 20 should be less than 68 and this represented by

8m + 20 < 68

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Answer:

OB

Step-by-step explanation:

The slopes are not changed.

See the picture of the 2 graphs.  The slopes are the same,, but the y intercepts are different, so the lines are parallel.

The angle x of the triangle is 68 degrees and the side y is 7.5 units.

The triangle ABC is a right angle triangle because it has one angle as 90 degrees. The sum of the angles in the triangle is 180 degrees.

The angle ECD is congruent to angle ACB(vertically opposite angles).

Therefore,

∠ECD ≅ ∠ACB

Hence,

x = 180 - 90 - 22

x = 68 degrees.

using trigonometric ratios, let's find y

cos 22 = adjacent / hypotenuse

sin 22 = 2y - 1 / 15

cross multiply

15 cos 22 = 2y - 1

2y - 1 = 13.9077578185

2y = 13.9077578185 + 1

2y = 14.9077578185

divide both sides by 2

y = 14.9077578185 / 2

y = 7.45387890925

Therefore,

y = 7.5 units

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Answer: He used 5 3/4 kg in all. There was 9 1/4 kg left.

Step-by-step explanation:

Add 3 1/2 and 2 1/4 to find how much he used. The common denominator is 4 so convert 3 1/2 to 3 2/4. Then add. The answer will be 5 3/4.

Subtract 5 3/4 from 15 to get how much is left. The answer will be 9 1/4.

Answer: It should be $101.18

Step-by-step explanation:

You would basically subtract the 81.60 to the 24% making it 19.58. then from the 19.58 you add the 81.60 and there you go!

a) The number of ways that she can arrange the 9 paintings is; 362880 ways

b)  If she only wants to display 5 of the paintings, the number of ways can she choose the paintings she wishes to display is; 126

c) The number of ways can she arrange 5 out of 9 paintings is; 120

a) If we take 9 paintings to be hung in 9 spaces arranged side by side, then it means that the first space can have any one of the 9 paintings, the second space can have any one of the remaining 8 paintings (as 1 is already hung), the third space can have any one of the remaining 7 paintings (as 2 already hung) e.t.c

Thus;

Number of ways to arrange all the paintings from left to right = 9! = 362880

b) We are now told that she only wants to display 5 of the paintings. Thus;

Number of ways she can choose the paintings she wishes to display is done by the combination formula;

nCr = n!/(r!(n - r)!)

9C5 = 9!/(5!(9 - 5)!)

= 126 ways

c) Any 5 of the 9 paintings can be arranged in;

5! = 120 ways

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The graph shown in the question is representing the equation y = log x, so option 3 is correct.

A collection of objects is arranged in a graph, where some object pairings are conceptually "linked." Each pair of connected vertices is referred to as an edge, and the objects are represented by mathematical abstractions known as vertices.

Given:

The graph is shown in the image,

Put the value of x and y from the graph to the equation as shown below,

x = 1, y = 0

Put in option 1,

y = log5 x

0 = log5

0 = 0.69

Again, put in option 2,

y = log x

0 = log1

0 = 0

Hence, it is the correct option.

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Answer:

162 units³

Step-by-step explanation:

Original solid:

V = 6 units³

SA = 22 units²

Dilated solid:

V = ?

SA = 198 units²

The ratio of the areas is 198/22 = 9

The ratio of the area is the square of the scale factor.

The scale factor is:

scale factor = √9 = 3

The ratio of the volumes is the cube of the scale factor.

ratio of volumes = 3³ = 27

The dilated volume is:

6 × 27 = 162 units³

Answer: 162 units³

Answer:

y = 2x + 1

1. Find the slope;  (change in y values)/(change in x values)

Slope = (-5 - 3)/ (-3 - 1) = -8/-4 = 2

2. Find the y-intercept (b) using  the slope intercept formula: y = mx + b

   m = 2 and using point (1, 3) , solve for "b"

      y = mx + b

      3 = 2(1) + b

      3 = 2 + b

     1 = b

3.  Write the linear equation: y = 2x + 1

Step-by-step explanation:

The practical domain of the function :

All integers from 1 to 8 and the set of f(r) is

f(r) = {76, 126, 176, 226, 276, 326, 376, 426}

What are domain and range of a function ?

The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

Since Rachel has 26 dimes at the start, this would translate as the y-intercept. Or the value of y when x is zero. In this case, when she has no rolls of dimes., she would still have 26. Since each roll has 50 dimes. each, the function that models the number of dimes. Rachel will have is

f(r) = 50r + 26

If she can only afford 8 rolls, then the maximum number of dimes Rachel will have is:

f(8) = 50(8) + 26 = 426 dimes

The practical domain of the function :

all integers from 1 to 8

Substitute r=1 to 8 into the equation and find f(r).

{76, 126, 176, 226, 276, 326, 376, 426}

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Answer: -7

Step-by-step explanation:

First, simplify the equation and make y isolated.

4x + y = -7

y = -7 - 4x

Plug in 0 for x.

y = -7 - 4(0)

y = -7